In ΔАBC, &ang;C = 90° and AC = BC; then AB2 is equal to ______.

In ΔАBC, &ang;C = 90° and AC = BC; then AB2 is equal to 2AC2. Explanation: By applying Pythagoras’ theorem to right-angled ΔABC where &ang;C = 90°, we get: AB2 = AC2 + BC2. Since it is given that AC = BC, substituting BC with AC gives AB2 = AC2 + AC2 = 2AC2.

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In ΔАBC, ∠C = 90° and AC = BC; then AB2 is equal to ______.

Question

In ΔАBC, ∠C = 90° and AC = BC; then AB² is equal to ______.

Options

AC²
2AC²
BC²
2BC² − AC²

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Solution

In ΔАBC, ∠C = 90° and AC = BC; then AB² is equal to 2AC².

Explanation:

By applying Pythagoras’ theorem to right-angled ΔABC where ∠C = 90°, we get: AB² = AC² + BC². Since it is given that AC = BC, substituting BC with AC gives AB² = AC² + AC² = 2AC².